General National Maritime Transport Co (GNMTC) is said to be in talks to replace the vessels in deals that could be worth more than $100m.
The moves comes just two months after the Libyan company agreed to dispose of its two oldest tankers.
The state-controlled tanker owner is said to have sent out a notice earlier this year with seeking high-specification aframax tankers, equipped with scrubbers and built to the International Maritime Organization's newer Tier III emission standards.
